Excel Models
Expected Spot Price
How can we assess the market’s expectation about the future change in the price of an asset?
For example, if today the spot price of one ton of copper is $10,125, while the 3-month futures price is $10,275, what does this tell us about the market’s expectations over the next three months? Does the market expect prices to rise or fall? By how much?
This question can be answered from the perspective of modern financial theory. I mean the CAPM model, which says that the greater the systematic (non-diversifiable) risk in an investment, the greater the expected return demanded by investors.
Suppose a trader buys a futures contract lasting T periods, hoping that when the contract expires, the future spot price will be high enough to make a profit. We assume that at the same time the trader enters the futures contract, they place the equivalent amount into a risk-free deposit, which accrues interest at the risk-free rate over the period. This ensures that at maturity the contract value is covered. In this way, the investment has the following cash flows:
-Foe-rT + ST
Now, let’s say we want to evaluate this investment. To do so, we take the expected spot price (E(S_T)) and discount it by the appropriate rate of return (k). The full picture looks like this:
Assuming the market is efficient and investments are priced so that NPV = 0, we get the relationship:
This formula links the futures price of an asset to the market’s expectation of its future spot price. The key variable here is the discount rate (k), which—as noted earlier—depends on the systematic risk of the investment (in this case, the asset’s price).
From the formula it follows:
- If systematic risk is zero → futures price equals expected spot price.
- If risk is high → the expected spot price exceeds the futures price.
- If risk is negative → the expected spot price is below the futures price.
What does “high risk” mean here? In our context, it means the asset’s price is positively correlated with the overall market. The stronger the correlation, the higher the risk. Zero correlation corresponds to the risk-free rate; negative correlation corresponds to lower risk and a lower required rate of return.
Keynes and Hicks
Another interesting perspective on the relationship between expected spot prices and futures prices was presented by economists John Maynard Keynes and John Hicks (see A Treatise on Money, 1930, and Value and Capital, 1939).
They argued that the expected price depends on the need for risk hedging. The logic is as follows:
- When traders expect higher future prices, they enter long futures contracts. On the other side of these contracts stand hedgers. These are market participants who also expect higher future spot prices but, for insurance purposes, are still willing to sell through futures contracts. For example, a copper producer might believe prices will rise beyond the current futures price, but still signs today’s futures contracts to reduce risk.
- Conversely, when the expected price is lower than the futures price, traders go short on futures, because there are business entities willing to sign more expensive futures contracts for hedging reasons.
Mean Reversion
Consumer commodities’ prices are characterized by a tendency to revert to the mean. Analysts often calculate a 5–10 year moving average. The tendency to return to the average price is determined by a dual pressure from both demand and supply sides:
If the price is very high, producers are incentivized to extract more — it becomes justifiable to open new and more complex deposits, increase recycling, etc. In other words, supply rises… On the other hand, when the price is high, it discourages consumption… due to high costs, projects are postponed, i.e., demand decreases.
The opposite process takes place when the price is low. Producers have minimum marginal costs, below which extraction is no longer feasible. As a result, inventories shrink, i.e., supply decreases. On the other hand, a low price itself triggers higher demand, creating new areas where the use of the commodity becomes profitable.
P.S.
Let’s return to the question posed at the beginning about the expected price of copper. What conclusions can we draw:
- Generally, copper is positively correlated with the economy (see chart). Accordingly, its expected price should be above the futures price.
- In a specific situation, the expected price depends on which side traders and consumers are positioned. If traders are shorting and consumers are hedging risks, the market anticipates a price decline.
- Since copper is predominantly a consumer commodity (rather than an investment one), its price is driven by the forces of demand and supply like a tailwind toward the long-term average.
Source: Options, Futures & Other Derivatives, John C. Hull